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Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial. (English) Zbl 0921.34032
The authors study the isochronous centers of two-dimensional autonomous systems in the plane $$\dot x= -y+X_s(x, y),\quad \dot y=x+Y_s(x,y),$$ where $X_s(x,y)$ and $Y_s (x,y$) are homogeneous polynomials of degree $s=4.$ A center is isochronous if the period of all integral curves in a neighborhood of the origin is constant. Necessary conditions for such isochronous center are obtained. Reversible systems that have an isochronous center at the origin are studied.

34C05Location of integral curves, singular points, limit cycles (ODE)
34A05Methods of solution of ODE
Full Text: DOI
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